The Mechanized Semantic Library is a collection of mathematical techniques
useful for developing semantic models of program logics and type systems:
separation algebras, permission share models,
indirection theory (a clean axiomatization of step indexing),
and modal logics.
The library has a special emphasis on techniques which integrate smoothly into a mechanical theorem prover; at the moment the library is only available for use in Coq.
MSL v0.2 has the following enhancements over v0.1:
The Mechanized Semantic Library is made available under a BSD-style license.
|1.||Base||Axioms for computation; custom tactics; basic theorems|
|2.||Separation Algebras||Compositional semantic models for separation logic||, , |
|4.||Shares||Share accounting to model fractional ownership in separation logic|||
|5.||Indirection Theory||Semantic models for approximating contravariant circularities||, |
|6.||Logics||Definitions of substructural and modal logics||, , , |
|||Multimodal Separation Logic
for Reasoning About Operational Semantics
|R. Dockins, A. W. Appel, A. Hobor||BibTeX|
|||A Fresh Look at Separation Algebras and Share Accounting||R. Dockins, A. Hobor, A. W. Appel||BibTeX|
|||A Theory of Indirection via Approximation||A. Hobor, R. Dockins, A. W. Appel||BibTeX|
|||A Logical Mix of Approximation and Separation||A. Hobor, R. Dockins, A. W. Appel||BibTeX|
List order is by publication date. For a mapping of files to papers please see the file list.
The MSL includes some associated examples using various components of the library. The first example, released with v0.2, is a mechanized type soundness proof for the polymorphic lambda calculus with references. We plan to include more examples as we continue to build the MSL. These examples are released under the same BSD-style license as the MSL.
|1||Type Soundness of the Polymorphic Lambda Calculus with References||Indirection Theory, Logics|
The following projects use the MSL. Although the MSL is utilized in them, and in some cases was developed in conjunction with them, they are independent projects, with their own developers, goals, codebase, and associated license schemes.
The goal of the Concurrent C Minor Project is to connect machine-verified source programs in sequential and concurrent programming languages to machine-verified optimizing compilers.
|#||File name||Component||Associated paper(s)|
|4.||sepalg_generators.v||Separation Algebras||, , |
|12.||knot_sa.v||Indirection Theory||, |
|19.||predicates_hered.v||Logics||, , , |
This file contains the axiom base for the development. We assume the classical axiom, dependent unique choice, relational choice, functional extensionality and propositional extensionality. However, the proofs in this distribution use only the extensionality axioms.
This exports the parts of the Coq standard library used throughout the development as well as a few custom convenience tactics.
This file defines our relational form of separation algebras with the disjointness axiom. We also define the join_sub relation and the joins relation. Additionally, elementary lemmas about the definitions are proved.
We define SA operators in this file. All the operators mentioned in , , and  appear here, along with a few others.
This file defines boolean algebras from an order-theoretic perspective. We also define axioms relating to properties we desire of share models, including relativization, splitting and token factory axioms.
Here we construct the boolean-labeled tree share model as discussed in . Note, however, that the proof of the token counting axioms follow a slightly different path than the proof in that paper. This is mostly because reasoning about sets in Coq is inconvenient.
This file simply repackages the construction from tree_shares.v into a nicer interface for downstream users. We also define the notion of a "positive" share; that is a nonunit share.
This file contains the central "knot" development used to model approximations to contravariant circularities. Included are both the axiomitization and the model construction. It follows section 8 of  quite closely.
Enhances knot.v by threading a monotonicity property through the construction. The result is that all predicates extracted from a knot are automatically hereditary. Although the axiomatization is not much more complex than in the basic case, the construction is significantly harder. The axiomatization is explained in section 2.3 of ; the construction will be explained in a future paper.
Enhances knot_hered.v to allow the input to the knot to be a bifunctor, and allow the user to supply a relation that further restricts the predicates that can be stored in the knot. The axiomatization is slightly more complicated than in the knot_hered case, but the construction is again more complicated. This file will be explained in a future paper.
Easy lemmas that follow from the theory of indirection, including a Galois connection.
The definition of a separation algebra on top of knots as coved in section 7 of  and in more detail in sections 6 and 7 of .
Used when you want to use the logics module, but do not have interesting separation behavior.
This file specializes the knot, knot_lemmas, and knot_sa files to use "Prop" as truth values.
A technical development of "unmapping" needed to get the extra unage* properties in knot_sa as explained in section 7 of .
An alternate, axiom-free, development of the knot. We avoid the need for the extensionality axiom by working explicitly up to equivalance relations and weakening the axioms of the theory accordingly.
The development of the uniqueness proof for knots. We prove that any two implementations of the theory of indirection are isomorphic.
We enhance separation algebras with a notion of aging as in sections 2 and 6 of . The "ASA" typeclass presents an interface sufficient to define the Kripke model below. The interface is implemented using the properties obtained from knot_sa.
Definition of the higher-order modal separation logic as discussed in sections 2, 4, 5, and 6 of ; section 4 of ; sections 5, 6, and 7 of ; and sections 3 and 6 of .
Lemmas about fashionable implication. This is partially explained in section 4 of .
Definition and proofs about equirecursion. We include both the standard "mu" recursion as well as a more powerful higher-order variant. This file is partially explained in section 4 of  and will be explained in more detail in a future paper.
A collection of utility lemmas for proving that various predicate functions are contractive or nonexpansive (for both the regular recursion and the higher-order variety). This file is partially explained in section 4 of  and will be explained in more detail in a future paper.
A file which re-exports the major components of the MSL library for users.
Copyright (c) 2009, Andrew Appel, Robert Dockins and Aquinas Hobor.
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